Some difference sequences defined by a sequence of modulus functions.
Keywords:Difference sequence spaces, A sequence of modulus functions
The idea of difference sequence spaces was introduced by Kizmaz , and this concept was generalized by Bektas and Colak . In this paper, we define the sequence spaces and , where F = (fk) is a sequence of modulus functions, and examine some inclusion relations and properties of these spaces.
Bektas, Cigdem, A. and Colak, R., Generalized difference sequence spaces defined by a sequence of modulli, Soochow J. Math., 29(2), pp. 215-220, (2003).
Et., M. and Colak, R., On some generalized difference sequence spaces, Soochow J. Math., 21, pp. 377-386, (1995).
Gaur, A. K. and Mursaleen, Difference sequence spaces, Internat. J. Math. & Math. Sci., 21(4), pp. 701-706, (1998).
Gnanaseelan, C. and Srivastava, P. D., The α−,β−,γ−duals of some generalized difference sequence spaces, Indain J. Math., 38(2), pp. 111-120, (1996).
Kamthan, P. K. and Gupta, M., Sequence spaces and series, Lecture Notes in Pure and Applied Mathematics, vol. 65 , Marcel Dekker, New York, (1981).
Kizmaz, H., On certain sequence spaces, Canad. Math. Bull. 24, pp. 169-176, (1981).
Kolk, E., Inclusion theorems for some sequence spaces defined by a sequence of modulli, Acta Comment. Univ. Tartu, 970, pp. 65-72, (1994).
Maddox, I. J., Some properties of paranormed sequence spaces, J. London Math. Soc. 1, pp. 316-322, (1969).
Maddox, I. J. , Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phil. Soc., 64, pp. 431-435, (1969).
Maddox, I. J., Elements of Functional Analysis, 2nd Edition, Cambridge University Press, (1970).
Maddox, I. J., Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100, pp. 161-166, (1986).
Oztürk, E. and Bilgen, T., Strongly summable sequence spaces defined by a modulus, Indian J. Pure Appl. Math. 25(6), pp. 621-625, (1994).
Ruckle, W. H., FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25, pp. 973-978, (1973).
How to Cite
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.